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a) x2 - 2xy + y2 - 4m2 + 4mn - n2 = (x - y)2 - [(2m)2 - 2.2m.n + n2] = (x - y)2 - (2m - n)2
= [(x - y) - (2m - n)][(x - y) + (2m - n)] = (x - y - 2m + n)(x - y + 2m - n)
b) x2 - 4x2y2 + y2 + 2xy = x2 + 2xy + y2 - 4x2y2 = (x + y)2 - (2xy)2 = (x + y - 2xy)(x + y + 2xy)
c) x6 - y6 = (x3)2 - (y3)2 = (x3 - y3)(x3 + y3) = (x - y)(x2 + xy + y2)(x + y)(x2 - xy - y2)
d) 25 - a2 + 2ab - b2 = 25 - (a2 - 2ab + b2) = 52 - (a - b)2 = (5 - a + b)(5 + a - b)
a: Ta có: \(x^2+2xy+y^2-4x^2y^2\)
\(=\left(x+y\right)^2-4x^2y^2\)
\(=\left(x+y+2xy\right)\left(x+y-2xy\right)\)
b: Ta có: \(x^6-y^6\)
\(=\left(x^3-y^3\right)\left(x^3+y^3\right)\)
\(=\left(x-y\right)\left(x+y\right)\left(x^2-xy+y^2\right)\left(x^2+xy+y^2\right)\)
c: Ta có: \(25-a^2+2ab-b^2\)
\(=25-\left(a-b\right)^2\)
\(=\left(5-a+b\right)\left(5+a-b\right)\)
d,=(2bc+b2+c2−a2)(2bc−b2−c2+a2)
=[(b+c)2−a2][−(b+c)2+a2]
=(b+c−a)(b+c+a)2(a−b−c)
\(a^2-b^2+4bc-4c^2\)
\(=a^2-\left(b^2-4bc+4c^2\right)\)
\(=a^2-\left(b-2c\right)^2\)
\(=\left(a-b+2c\right)\left(a+b-2c\right)\)
1
a, 2x2+4x+2-2y2 = 2(x2+2x+1-y2)= 2[(x+1)2-y2 ] = 2(x-y+1)(x+y+1)
b, 2x - 2y - x2 + 2xy - y2= 2(x -y) - (x2 - 2xy + y2) = 2(x-y)-(x-y)2=(x-y)(2-x+y)
c, x2-y2-2y-1=x2-(y2+2y+1)=x2-(y+1)2=(x-y-1)(x+y+1)
d, x2-4x-2xy-4y+y2= x2-2xy+y2-4x-4y=(x-y)
2.
a, x2-3x+2=x2-x-2x+2=x(x-1)-2(x-1)=(x-2)(x-1)
b, x2+5x+6=x2+2x+3x+6=x(x+2)+3(x+2)=(x+3)(x+2)
c, x2+6x-6=
Kai Parker